Readout of strongly coupled NV center-pair spin states with deep neural networks

J\"org Wrachtrup; Matthew Joliffe; Vadim Vorobyov

REVIEW 4 major objections 4 minor 1 cited by

Readout of strongly coupled NV center-pair spin states with deep neural networks

T0 review · 4 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A deep neural network trained on photon-count histograms reads out the collective spin state of two strongly coupled NV centers in a single shot, including the spin-spin correlation.

desk verdict A credible proof-of-concept for neural-net demultiplexing of unresolved NV pairs, with unquantified readout fidelity due to unverified training labels. read the letter →

arxiv 2412.19581 v1 pith:D6LSJUTZ submitted 2024-12-27 quant-ph physics.data-an

Matthew Joliffe , Vadim Vorobyov , Jörg Wrachtrup This is my paper · ORCID

classification quant-phphysics.data-an

keywords NVcenterpairspin-to-chargeconversionsingle-shotreadoutdeepneuralnetworkphoton-counthistogramquantumsensingstrongcouplingmachinelearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that two nitrogen-vacancy (NV) centers in diamond, spaced about 10 nanometers apart and strongly coupled through their magnetic dipoles, can be read out together even though they lie within one diffraction-limited spot. The readout uses spin-to-charge conversion to map each spin onto a long-lived charge state, then feeds the measured photon-count histogram into a trained deep neural network. The network outputs the probabilities of the four joint spin states, from which the single-spin expectation values and the spin-spin correlation $\langle S_z^{(1)} S_z^{(2)}\rangle$ follow. This matters because strongly coupled spin clusters are too close for ordinary confocal imaging, so a readout that works without resolving the individual emitters removes a bottleneck for nanoscale quantum registers and correlation sensing.

What carries the argument

The key machinery is a spin-to-charge conversion protocol combined with a convolutional neural network as a statistical decoder. Spin-to-charge conversion uses a 594 nm pulse to cycle the spin, a 638 nm pulse to ionize the $m_s=0$ state while the $m_s=1$ state is sheltered in the metastable singlet, and a low-power 594 nm readout; the resulting photon counts form a histogram with four overlapping peaks corresponding to the two NV charge states. The neural network, built from one-dimensional convolution and max-pooling layers followed by dense layers and trained with mean-square error plus L2 regularization, maps the normalized histogram directly to the probabilities of the four joint spin states, bypassing the analytic model of charge-switching dynamics given by the convolution $p(n,k_1,k_2)=\sum_i p_1(N=i,k_1)p_2(N=n-i,k_2)$.

What would settle it

Prepare the same two-spin states with an independent, tomographically verified protocol, for example interleaved randomized benchmarking or DEER-calibrated pulses, and compare the network's inferred probabilities and correlations with the verified values; any systematic offset would show the readout is learning the nominal preparation labels rather than the physical states. A simpler check is to measure the network's predicted $\langle S_z\rangle$ versus pulse area over a full Rabi oscillation and look for deviations from the expected sinusoidal curve at angles not used in training.

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Extended reading notes

Core claim

The central claim is that collective states of an unresolved, strongly coupled NV pair become accessible in a single-shot measurement once the photon-count distribution of the spin-to-charge-converted readout is interpreted by a neural network. For an NV pair with coupling $g\approx 2\pi\cdot 50\,\mathrm{kHz}$ and spacing $d\sim 10\,\mathrm{nm}$, the four joint spin states produce overlapping but distinguishable charge-state readout histograms. The network, trained on histograms of nominally prepared Rabi states, predicts the occupation probabilities of the four basis states; the paper verifies this on held-out test data and on rotations with pulse areas $\theta=\{0,1/4,1/2,3/4,1\}\pi$. From those probabilities it reconstructs $\langle S_z^{(1)}\rangle$, $\langle S_z^{(2)}\rangle$, and $\langle S_z^{(1)}S_z^{(2)}\rangle$, and demonstrates that a zero-mean correlated signal applied to both spins leaves the correlation nonzero while the individual expectations average to zero.

Load-bearing premise

The network's training labels are the spin states that the microwave pulses are assumed to prepare, with no independent verification that the actual initialization and rotation match the nominal pulse areas; if they do not, the learned readout inherits the error without the experiment noticing.

Editorial extensions

If this is right

The joint state of two diffraction-unresolved NV centers can be read out through the single-shot spin-to-charge technique, giving access to the collective register space rather than only to individual spin signals.
The trained network returns the single-spin expectation values and the spin-spin correlation from the measured histograms, enabling direct parity measurements.
A correlated zero-mean signal applied to both spins is detectable through the correlation even though the averaged single-spin responses vanish, a proof of concept for nanoscale covariance sensing.
Because the network learns from histograms rather than from an analytic model, the approach extends more easily than fitting the charge-switching model, with numerical simulations showing useful training up to clusters of about five emitters.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same histogram-to-state decoder could be transferred to other color-center or qubit platforms whose readout is a multiplexed stochastic photon channel, provided training states can be prepared; the paper mentions scanning probe and quantum register settings but does not demonstrate them.
Because the network is trained on nominal preparation labels, its prediction confidence on out-of-distribution histograms could serve as a built-in diagnostic for state-preparation errors, an extension the paper does not make.
The scaling simulation suggests that the limiting resource is not optical resolution but the multiplicity of distinguishable emission or switching rates, so engineering distinct charge-switching rates could push the cluster-size ceiling beyond five; this is an inference from the paper's Pearson-coefficient drop at cluster size six.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a credible proof-of-concept that a convolutional network can demultiplex two strongly coupled NV centers from single-shot photon-count histograms, and the held-out data look honest. What is missing is a quantified readout fidelity and any independent check on the training labels.

The genuinely new piece is applying a deep network to the photon-count histogram of an unresolved pair, combined with the polarization-based brightness asymmetry that makes the two charge-state channels distinguishable. Prior work does single-spin spin-to-charge readout and covariance magnetometry, but not this demultiplexing. The rotation curves in Fig. 4a behave as expected, the correlated-signal sensing works, and the scaling simulation to three to five centers is a useful sanity check. Credit where due: the authors openly state that the Pearson score collapses at six defects, which is the kind of limitation statement you want to see.

The soft spot is the calibration of the training labels. The states are prepared by Rabi pulses of nominal area, starting from an assumed |00> state, and there is no independent measurement of initialization or rotation fidelity. If the actual spin state differs from the nominal one, the network simply learns the mapping between photon statistics and the supplied labels. A held-out test set drawn from the same label convention will not catch a systematic pulse-area error. The paper reports no per-basis-state readout fidelity, no confusion matrix, and no comparison against the analytical model of Eq. (1). The vanishing parity after a pi/2 pulse is consistent with the nominal sequence, so it does not serve as an independent verification. These are real gaps, but they are fixable with a calibration measurement or a cross-check against the analytical model.

Minor concerns: only one pair is demonstrated, no data or code are shipped, and the scaling study is idealized. None of that is fatal for a proof of concept.

My recommendation: send it to peer review. The idea is plausible, the experiment seems internally consistent, and the main weakness is addressable in revision. A referee should ask for quantified fidelity and for code/data to verify the training procedure. I would not cite it in its current form, but I would follow the revised version.

Referee Report

4 major / 4 minor

Summary. The paper claims that the collective spin states of two strongly coupled NV centers separated by roughly 10 nm and unresolved in confocal microscopy can be read out by feeding photon-count histograms from spin-to-charge conversion into a deep neural network. The network is trained on histograms labeled by nominal spin states prepared with Rabi-like pulses, and the authors demonstrate demultiplexed ODMR, state tomography via expectation values of single-spin operators and a correlation operator, and a proof-of-concept correlated-signal sensing measurement. Numerical simulations are used to argue that the approach can scale to clusters of up to about five NV centers, with performance degrading for larger clusters.

Significance. If the central claim is validated, the method would address a real bottleneck in spin-cluster readout: strong dipolar coupling requires nanometer spacing, which prevents conventional confocal resolution of individual emitters. The experimental demonstration of demultiplexed ODMR and the use of separate training and test datasets are genuine strengths, and the correlated-signal sensing proof of concept is a useful step toward covariance magnetometry. However, the absence of quantitative readout fidelities and of an independent calibration of the training labels leaves the central claim insufficiently supported, so the current manuscript does not yet establish the method as a calibrated measurement.

major comments (4)

[Section II (Fig. 3c, Fig. 4a)] The training labels are the nominal spin states assigned from Rabi-like microwave pulses, with no independent verification of initialization fidelity, pulse-area calibration, or the assumption that the initial state is |00>. Because the network is trained and evaluated on the same label convention, a systematic preparation error would be absorbed into the learned mapping and would not manifest as test error. The vanishing parity after a pi/2 rotation and the correlation results in Fig. 4c therefore do not by themselves establish calibrated readout. I ask the authors to report per-basis-state readout fidelities or a confusion matrix on the test set, and to compare the network predictions against an independent estimator on the same test histograms, for example the analytical model of Eq. (1) or a separate calibration measurement.
[Section II (Fig. 3c)] No quantitative performance metric is reported for the trained model. Fig. 3c shows only a scatter plot, without Pearson correlation, R^2, classification accuracy, or confidence intervals. Since the central claim is that the network can read out collective states, the manuscript should state the achieved fidelity or correlation score quantitatively, along with the number of test histograms used.
[Section II (Fig. 4a)] The term 'single-shot readout' is used in the abstract and introduction, but Fig. 4a averages 64 histograms per state and the network outputs class probabilities rather than a projective assignment for an individual shot. The authors should clarify what 'single-shot' means in this protocol and how the reported expectation values relate to single-shot classification, or avoid the term if it is misleading.
[Section III (Fig. 5)] The scaling simulations in Fig. 5 lack details needed to assess the claim that the method extends to clusters of five defects. The generative model for the simulated histograms, the label convention, the training/test split, and the network hyperparameters are not specified. In addition, Fig. 5d shows the Pearson score dropping close to zero for cluster size 6, so the statement that the method can be applied to 'large clusters up to five systems' should be backed by quantitative performance metrics and error bars for each cluster size.

minor comments (4)

[Section II] There are typographical errors: 'we we able' in the paragraph describing the TensorFlow model, and 'neccessary' in the Discussion. The Introduction also says 'electrical assisted readout with nanoscale contracts', which should likely be 'contacts'.
[Figure 1] The text refers to panels inconsistently: the polarization plot is labeled Fig. 1c but the text says 'Fig. 1c shows a continuous readout of the two NV system', and the histogram is labeled Fig. 1e but the text says 'Fig. 1d shows a histogram'. Please renumber the panels or correct the references.
[Section II (Fig. 4c)] The correlated-signal sensing measurement is described only briefly. The number of repetitions, the randomization procedure for the 0 and pi pulses, and the data-processing steps should be specified so that the experiment can be reproduced.
[Appendix A] The training details are incomplete: the loss function appendix mentions L2 regularization and the architecture, but does not give the learning rate, batch size, number of epochs, regularization strength, or the number of training histograms. Please add these parameters.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the neural-network readout is trained and tested on separate datasets, and the cited analytical model is not the source of the spin-state predictions.

full rationale

The paper's central claim is an experimental demonstration of supervised machine-learning readout: photon-count histograms from spin-to-charge conversion are labeled by nominally prepared spin states, a convolutional network is trained on one set of histograms, and its performance is evaluated on a separate held-out set (Fig. 3c). This is a standard train/test split; the predictions are not obtained by re-inserting the training labels, and the reported expectation values and correlations are linear functions of the network outputs, not fitted parameters renamed as predictions. The analytical charge-switching model of Eq. 1 is cited from prior work including the authors' own Ref. [14], but it is used only to characterize charge-state dynamics and optimize laser parameters; the network learns the histogram-to-state mapping directly from data, so this self-citation is not load-bearing for the readout claim. The only substantive concern is that the ground-truth labels are the nominal Rabi-prepared states, with no independent calibration of initialization or rotation fidelity. That is an experimental validity limitation, not a circular derivation: the network could fit incorrect labels and still achieve low test loss, so the prediction is not equivalent to the input by construction. Because no specific equation or fitted parameter reduces to the claim, no circular step can be exhibited.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a calibrated experimental protocol: independent charge switching, a 30% metastable-singlet protection probability for spin-to-charge conversion, and correct training labels from Rabi pulses. It also depends on the learned NN weights and hand-chosen hyperparameters. No new physical entities are introduced.

free parameters (4)

Charge-switching rates of NV1 and NV2 (ionization/recombination) = Not listed numerically; extracted from fits of Eq. (1) to histograms at several 594 nm laser powers (Fig. 2a,b)
These rates are fitted to the measured two-emitter histograms and are used to choose the laser power and readout time for the protocol.
Brightness ratio between NV1 and NV2 = About 2:1, set by rotating excitation polarization
The polarization is aligned so that NV1 is roughly twice as bright as NV2 (Sec. II, Fig. 1c), creating histogram peak separation used by the classifier.
Neural network hyperparameters = 1D convolution with 64 channels and kernel size 10, max pooling, dense layers of 64 and 128, dropout; exact epochs and…
The architecture and regularization penalty (L2 in Fig. 3a) are chosen by hand and affect the reported readout performance.
Trained neural network weights = Learned via TensorFlow; not shipped
The output probabilities are entirely determined by these fitted weights; without them the model cannot be reproduced.

assumptions (4)

domain assumption The charge-state switching events of the two NV centers are independent, so the joint photon-count distribution is the convolution of two single-emitter distributions as written in Eq. (1).
The paper states this assumption immediately before Eq. (1). Correlated switching would bias the rate calibration and the histogram model.
domain assumption The metastable singlet state protects the ms=1 spin from the 638 nm ionization pulse with about 30% probability, while ms=0 is ionized with high probability.
This spin-to-charge conversion mechanism is stated in Sec. II (Fig. 2c) and is taken from prior single-NV work cited as Refs. [14,21].
domain assumption Rabi-like microwave pulses with nominal area theta prepare the intended two-spin product states used as training and test labels.
Used in Figs. 3b and 4a. There is no independent state-tomography check of the preparation, so errors in pulse calibration propagate into the labels and the learned readout.
domain assumption The readout is projective along Sz, so a histogram from any prepared state is a mixture of the four basis-state histograms.
The NN is trained only on basis states but applied to fractional rotations and mixtures; this assumes the single-shot measurement collapses the spin and that the histogram mixture model is valid.

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Cite this review

Pith. "Pith review of Readout of strongly coupled NV center-pair spin states with deep neural networks." pith.science (2026). https://pith.science/paper/D6LSJUTZ

@misc{pith2026241219581,
  author       = {Pith},
  title        = {Pith review of: Readout of strongly coupled NV center-pair spin states with deep neural networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D6LSJUTZ}},
  note         = {Machine review of arXiv:2412.19581}
}

read the original abstract

Optically addressable electron spin clusters are of interest for quantum computation, simulation and sensing. However, with interaction length scales of a few tens of nanometers in the strong coupling regime, they are unresolved in conventional confocal microscopy, making individual readout problematic. Here we show that when using a single shot readout technique, collective states of the combined register space become accessible. By using spin to charge conversion of the defects we draw the connection between the intricate photon count statistics with spin state tomography using deep neural networks. This approach is particularly versatile with further scaling the number of constituent spins in a cluster due to complexity of the analytical treatment. We perform a proof of concept measurement of the correlated classical signal, paving the way for using our technique in realistic applications.

Figures

Figures reproduced from arXiv: 2412.19581 by the authors.

**Figure 2.** FIG. 2. Charge switching dynamics of an NV pair and their spin to charge conversion for readout demultiplexing. a) Histogram [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** c. It is important that the training and test data are kept separate to ensure that model doesn’t overfit and its predictions can be generalized. Fig. 3d shows the basis state histograms. It is evident that the histograms have a lot of overlap and a bias in the basis states representation, for example the first peak corresponding to the "00" charge state always has the predominant contribution to the signal. The f… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. Tomography of the states and sensing. a) NV center pair prepared into the 00 state and then a fractional pulse is [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Scaling of the method to larger cluster sizes (numerical simulation) a) Simulated photon histograms for various number [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. a) Loss function evolution upon training of the model for the experimental case of NV center pair b) Double electron [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

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D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, Quantum technologies with optically interfaced solid-state spins, Nature Photonics12, 516 (2018)

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